This is a book for statistical practitioners, particularly those who design and analyze studies for survival and event history data. Its goal is to extend the toolkit beyond the basic triad provided by most statistical packages: the Kaplan-Meier estimator, log-rank test, and Cox regression model. Building on recent developments motivated by counting process and martingale theory, it shows the reader how to extend the Cox model to analyse multiple/correlated event data using marginal and random effects (frailty) models. It covers the use of residuals and diagnostic plots to identify influential or outlying observations, assess proportional hazards and examine other aspects of goodness of fit. Other topics include time-dependent covariates and strata, discontinuous intervals of risk, multiple time scales, smoothing and regression splines, and the computation of expected survival curves. A knowledge of counting processes and martingales is not assumed as the early chapters provide an introduction to this area. The focus of the book is on actual data examples, the analysis and interpretation of the results, and computation. The methods are now readily available in SAS and S-Plus and this book gives a hands-on introduction, showing how to implement them in both packages, with worked examples for many data sets. The authors call on their extensive experience and give practical advice, including pitfalls to be avoided. Terry Therneau is Head of the Section of Biostatistics, Mayo Clinic, Rochester, Minnesota. He is actively involved in medical consulting, with emphasis in the areas of chronic liver disease, physical medicine, hematology, and laboratory medicine, and is an author on numerous papers in medical and statistical journals. He wrote two of the original SAS procedures for survival analysis (coxregr and survtest), as well as the majority of the S-Plus survival functions. Patricia Grambsch is Associate Professor in the Division of Biostatistics, School of Public Health, University of Minnesota. She has collaborated extensively with physicians and public health researchers in chronic liver disease, cancer prevention, hypertension clinical trials and psychiatric research. She is a fellow the American Statistical Association and the author of many papers in medical and statistical journals.